Are you a Zombie? A Supervised Learning Method to Classify Unviable Firms and Identify the Determinants

Are you a Zombie? A Supervised Learning Method to Classify Unviable Firms and Identify the Determinants ∗

Angela De Martiis † Thomas L.A. Heil ‡ Franziska J. Peter §

This draft: December 16, 2020

Abstract

We examine the determinants of zombie companies using a comprehensive firmlevel data set of public corporations from Europe and the United States. We show that US zombie companies differ from their European peers on a number of firmspecific and industry-specific factors. Using decision trees, we document that income and leverage-related variables are among the main drivers classifying zombie companies in Europe, while dividends and stock-related variables are the most important in the US. We observe a frequent mislabelling of zombie firms into other unviable types of firms. To account for this, we also examine the determinants of distressed firms and compare them to the zombies. We find that zombie and distressed are not comparable types of companies, rather companies at a different stage of their financial unviability. We also document that zombification is especially a European phenomenon, while distressed-type of firms are mostly populating the US economy. We find no major differences in terms of zombie company-specific determinants between crisis and non-crisis periods.

JEL codes: C55, C63, D22, E44, G32, G33

Keywords: zombie firms, financial constraint, decision trees, distressed firms

1 Introduction

Long after the global financial crisis, the phenomenon of zombie companies remains a concern and stirs up growing debates among scholars and policy-makers. Early studies define zombie firms as insolvent companies with little hope of recovery, but avoiding failure thanks to support from their banks (Hoshi 2006). Caballero, Hoshi, and Kashyap (2008) initially examined this misdirected lending mechanism in relation to the Japanese macroeconomic stagnation that began in the early 1990s.

Previous studies investigate the reasons why these companies remain alive and concentrate on the consequences of what became a widespread phenomenon. The media community often narrates about the rise of zombie companies that, supported by statebacked credit, spend their cash servicing debt instead of investing it. 1 There is evidence that the share of zombie firms has trended up since the late 1980s (Banerjee and Hofmann 2018; Adalet McGowan, Andrews, and Millot 2018). We also know that they appear to be linked to the downward trend in interest rates (Banerjee and Hofmann 2018) and to weak banks (Caballero, Hoshi, and Kashyap 2008; Giannetti and Simonov 2013; Schivardi, Sette, and Tabellini 2017; Storz, Koetter, and Setzer 2017; Andrews and Petroulakis 2017; Acharya, Eisert, et al. 2019).

Yet, we are still far from being able to understand the determinants of zombie firms. There are some evident drivers, such as the size of the company and the industry (Hoshi 2006). However, the existing literature lacks a thorough empirical investigation of the characteristics of such companies as well as the potential similarities and differences among zombie companies across countries and time.

Using a detailed and comprehensive set of publicly listed companies' firm-level data from Compustat North America and Compustat Global, we perform an immediate geographical inspection of the share of zombie companies. Figure 1 illustrates that the zombie phenomenon is not limited to a small subset of countries. Despite this fact, previous research has mostly focused on Japan or on a sample of specific countries (among others, Caballero, Hoshi, and Kashyap (2008), Adalet McGowan, Andrews, and Millot (2018), Banerjee and Hofmann (2018), Acharya, Crosignani, et al. (2019)). In this study, we cover 32 European countries plus the United States on a time frame of over two decades that allows us to observe several business cycles.

With this overview in mind, our empirical analysis delves deeper into the firm-specific characteristics of zombie companies. We start by identifying the companies that are considered zombies. This represents a crucial point, given that the existing literature lacks a disciplined approach towards identifying such unviable firms, often mislabelling them. We thus use two different definitions. The first rests on the interest coverage ratio (Adalet McGowan, Andrews, and Millot 2018), while the second one adds market expectations (Banerjee and Hofmann 2018). We use the latter measure to analyze the robustness of our results.

Next, to understand the country-specific firm-level determinants of zombie companies, we employ a supervised learning method: the classification trees. When applying decision trees to our high dimensional data set containing balance sheet, accounting and fundamental variables, we refrain from any a priori assumptions and instead let the data and algorithms select the main drivers. We repeat our analysis for different time periods in order to examine whether, and to which extent, the determinants vary throughout time. In addition, we repeat the same binary structure to carefully review and analyze the firm-specific determinants of distressed and non-distressed companies and compare the latter to zombie firms. To the best of our knowledge, this is the first study that employs such a refined machine learning method to explore the firm-specific characteristics and behavior of zombie firms across countries and time.

We also implement a set of multi-classification trees that allow us to examine systematic differences among zombie, distressed, recovered zombie, and healthy companies.

In particular, we examine empirically the firm-specific determinants of zombie companies in Europe and the United States and, differently from Hoshi (2006), we document that zombie firms are companies with healthy periods in-between financially unsound years and are likely to recover. In our data processing, by counting the zombie spells we observe that the zombies in the sample do recover.

We further show that US zombie companies differ from their European peers on a number of firm-specific and industry-specific factors. In this regard, we document that income and leverage-related variables are among the main drivers classifying zombie companies in Europe, while dividends and stock-related variables are predominant factors among US zombie companies populating the energy, real estate and software industry. These factors remain relevant during crisis and non-crisis periods. We also examine the firm-specific determinants of distressed and non-distressed firms. To the best of our knowledge, we are the first to show that zombie and distressed firms are not comparable types of companies, rather firms at a different stage of their financial unviability. The latter finding yield relevant policy-related implications given that zombies are often improperly treated as distressed-type of companies.

In addition, the classification trees document that zombification is especially relevant among the European economies, where zombie companies are more prevalent, followed by the healthy. To the contrary, distressed-type of firms are mostly populating the US market, where the two major classes are the distressed and the healthy companies.

This study contributes to four strands of literature. The first, relates to the literature examining the so-called zombie companies, a phenomenon that was first investigated in reference to the Japanese banking crisis of the 1990s. With this respect, Caballero, Hoshi, and Kashyap (2008) explore the zombie lending behavior, a process in which large Japanese banks often engaged in sham loan restructurings in order to keep the credit flowing to otherwise insolvent borrowers. As a result, an increase in zombie companies generated a depression of the investments and of the employment growth of healthy companies and distortions in the creation of jobs and productivity. Peek and Rosengren (2005) provide evidence that troubled Japanese banks allocated credit to highly indebted borrowers to avoid realizing the losses on their balance sheets. More recently, Adalet McGowan, Andrews, and Millot (2018) document an increase in the share of zombie companies also in the OECD economies, between 2003 and 2013. Schivardi, Sette, and Tabellini (2017) confirm that zombie companies obtained credit from undercapitalized banks, and Schivardi, Sette, and Tabellini (2020) highlight the identification challenges that come with the analysis of the zombie phenomenon. Hoshi (2006) identifies zombie companies in Japan and investigates some of their main characteristics in a set of probit regressions. Within these studies, we contribute by examining zombie companies in Europe and in the United States and by identifying the firm-level determinants of zombie companies with respect to non-zombies and, in a second stage, also with respect to distressed, recovered and healthy companies.

The second strand, relates to the literature on zombie companies and machine learning. Within this literature we are, to the best of our knowledge, the first to examine the determinants of zombie companies across countries and time using a supervised learning

algorithm that allows us to better classify and divide the zombies from the non-zombies and also from other firm categories such as distressed, recovered and healthy companies. This method allows us to account for many of the classification challenges pertaining to the zombie phenomenon. The large amount of data, assembled using Compustat Global and Compustat North America, proves impractical to analyze the most important determinants of zombie companies via classical statistical models. We thus exploit an algorithmic modeling, precisely classification trees-like algorithm, in order to find those important drivers out of a broad range of explanatory variables. Specifically, the algorithm behind a decision tree searches through the whole range of explanatory variables and subsequently finds the variables that better classify zombies versus non-zombies, or in a multi-classification tree setting the zombies from the distressed, the recovered and healthy firms. Within this strand, the only other paper using machine learning techniques to predict firm failure is the study of Bargagli Stoffi, Riccaboni, and Rungi (2020), who propose an alternative definition of zombies using a sample of Italian firms.

The third strand, draws upon the corporate finance literature examining firms' financial distress, the so called distressed firms. Within this sizable literature, at the intersection between finance and accounting, Altman (1968) and Ohlson (1980) are among the first to explore the concept of firm financial distress by proposing measurement techniques still widely used and recently complemented by market-value based measures, such as the one of Campbell, Hilscher, and Szilagyi (2008). We contribute to this literature by examining the firm-level determinants of distressed firms in Europe and in the United States and comparing them to zombie companies. In the existing literature zombie companies are often mislabelled as distressed-type of firms, we thus exploit our classification tree algorithm to observe whether distressed companies can be compared to zombie companies or whether relevant differences in terms of firm characteristics emerge. In performing this exercise, we confirm some of the known factors characterizing distressed companies, but we also shed light on unexplored differences between zombies and distressed that add to the empirical finance literature (Chan and Chen 1991; Campbell, Hilscher, and Szilagyi 2008; Skinner and Soltes 2011; Eisdorfer, A. Goyal, and Zhdanov 2018), by documenting, among other factors, that US zombie firms are determined by conservative dividend policies.

The last strand, relates to the literature examining regulatory and bankruptcy frameworks across countries. By analyzing the determinants of zombies and non-zombies across countries, the existence of differing regulatory regimes plays a crucial role as evergreening incentives are indeed stronger in countries with weak insolvency frameworks. Within the European countries, a more harmonized insolvency framework has the potential to make the long-term existence of zombie companies less of a concern. Within this literature, existing studies account for differences in bankruptcy codes when examining strategic defaults (Favara, Schroth, and Valta 2012) and levered firms (Acharya and Subramanian 2009), and also differences between civil law and common law countries (Djankov, McLiesh, and Shleifer 2007). We add to this literature by highlighting the role played by differing regulatory frameworks across countries. In this regard, we argue that the firm-specific differences between US and European public zombie corporations can be ex-

plained by unalike insolvency laws, where stringent insolvency regimes are more efficient at rehabilitating viable firms and liquidating non-viable ones (McGowan, Andrews, and Millot 2017).

The remainder of the paper proceeds as follows. Section 2 describes the data, defines alternative measures for zombie companies, discusses the rationale behind their existence and shows empirical evidence for their prevalence. Section 3 includes the analysis of determinants using decision trees, it outlines the methodology (3.1), presents the empirical analysis of zombie versus non-zombie decision trees (3.2), the classification trees of distressed versus non-distressed companies (3.3), followed by the multi-classification tree setting, where the firm-level determinants of zombie, distressed, recovered and healthy companies are analyzed (3.4), and finally provides a benchmark analysis using logistic regressions (3.5). Section 4 concludes.

2 Data, Measures, and Prevalence of Zombie Firms

2.1 Data

We use firm-level data from Compustat Global and Compustat North America. The first database provides financial and market data about active and inactive public companies from more than 80 countries, including coverage of over 96% of European market capitalization with annual data history that goes back to 1978. The second database covers publicly listed companies from the United States and Canada. The rich data allows us to gather financial, balance sheet and market data information covering several business cycle expansions and contractions in economic activity from the late 1980s to 2018. In addition, we add comprehensive stock price data from Thomson Reuters Datastream to Compustat Global data set using the international securities identification number, ISIN codes, for each company from 1990 to 2018.

In terms of data pre-processing, we restrict both data sets to the years 1996-2018 and delete the observations with a missing company unique identifier, the gvkey, and missing information on the fiscal year, fyear. We remove all gvkey-fyear duplicates and drop all variables that display missing values for more than 75% and 85% of their observations, thus leaving us with approximately 90 variables in both data sets. Following previous studies on zombie companies, we exclude all companies belonging to the utilities, financial, insurance and banking industries. 2 Last, we winsorize each variable at the 5% and 95% percentile and drop all observations below and above this threshold, in order to reduce the effect of outliers. We impute the remaining missing values and find that iterative regression imputation, as proposed by Buck (1960), produces the most promising results in terms of predictive power. 3 This data preparation process yields a well-stocked

data set consisting of 62227 observations for 32 European countries and 100250 for the United States.

With respect to firm-specific characteristics, we additionally compute a set of performance measures that are commonly used in the empirical finance literature to capture firm size, asset tangibility, profitability, risk, liquidity, market value and growth opportunities. We use the latter information to understand whether, and to which extent, these measures contribute to the classification of a company as a zombie. In Appendix A we report the description and definition of the variables used. 4

2.2 Zombie Measures

The existing literature provides different approaches to define a zombie company. Each of them has their own limitations, advantages and disadvantages. 5

Caballero, Hoshi, and Kashyap (2008) and Hoshi (2006) identify Japanese companies as zombies, whenever they receive subsidized credit, i.e. loans at advantageous interest rates, at rates below those of the most creditworthy companies. Fukuda and Nakamura (2011) add two criteria, profitability and evergreen lending, to avoid type one and two errors, while more recently Adalet McGowan, Andrews, and Millot (2018) adopt a measure based on the interest coverage ratio, an accounting measure that captures the persistent lack of profitability in mature companies. Banerjee and Hofmann (2018) add to the latter a measure of market expectations about the company's future profit potential, the Tobin's q. 6 Acharya, Crosignani, et al. (2019) and Acharya, Eisert, et al. (2019) use two criteria based on the interest coverage ratio and leverage of the company, plus the subsidized credit received by zombies.

Our first definition relies on the interest coverage ratio, a measure that is based on the financial operating characteristics of a company. 7 The interest coverage ratio, ICR it , for firm i , in year t , is computed as EBIT it ♥ IE it , where EBIT it is earnings before interest and taxes, and IE it denotes the interest expense, for each firm i at time t . 8 A company

7 If we look at the vast body of literature on financial distress, we find that different measurement techniques are provided. From the traditional accounting-based measures of Altman (1968) and Ohlson (1980), to the more recent market value-based measures of Campbell, Hilscher, and Szilagyi (2008). On this, a recent and comprehensive literature review summary on firm-specific financial distress is provided by Habib et al. (2020). We are interested in measuring zombie firms, which are measured differently to distressed firms. For the latter type of companies we adopt the Altman (1968) Z-score.

8 As per Compustat data, we use the variable xint as a measure of interest expense which represents the company's gross periodic expense in securing long- and short-term debt. From the established studies, both interest expense and interest payments (interest paid) are used to compute the ICR it (Adalet McGowan, Andrews, and Millot 2018; Banerjee and Hofmann 2018; Acharya, Crosignani, et al. 2019). We recall that the variable xint , as from Compustat Data Guide, includes also items such as:

is thus classified as zombie if its ICR it is less than one for at least three consecutive years and if it is a mature firm, meaning a company that is at least ten years old. The final measure is a binary variable.

Our second definition follows Banerjee and Hofmann (2018) who classify a firm as zombie whenever its ICR it is less than one for at least three consecutive years, its age is at least 10 years old and its Tobin's q is below median within a sector in a given year. 9

2.3 Rationale and Prevalence of Zombie Firms

Given the rich data set, we monitor the ups and downs in the recovery process of zombie companies. In doing this exercise, it becomes clear that in order to fully understand the zombie phenomenon it is crucial to analyze the recovered zombies, their healthy peers and compare the zombies to other unviable types of companies. Zombie firms are often treated as financially distressed companies, up to the point where the two are used interchangeably to denote one or the other. We, however, document that zombie firms differ from distressed companies, and should thus be treated differently.

In this setting, the healthy firms serve as our baseline group and are identified as those companies with an interest coverage ratio above one throughout the entire period of observation, meaning firms that were never zombie in their life, while distressed firms are, according to existing definitions, companies close to default (Altman 1968; Ohlson 1980; Gordon 1971). To measure distressed-type of firms we use the Altman Z-score measure (Altman 1968). The recovered are instead those that leave the zombie status at least once. We capture the recovered by counting the number of zombie spells in our firm sample. This allows us to observe whether zombie firms recover, and how often.

Table 1 reports descriptive statistics on a set of performance measures for our sample of companies in Europe and the United States. Zombie firms fall behind their healthy peers on a number of characteristics: they show differences and similarities to the distressed, while the recovered zombies prove growth potentials.

amortization of debt discount or premium, debt issuance expense (such as, underwriting fees, brokerage costs, advertising costs), discount on the sale of receivables of a finance subsidiary, factoring charges, finance charges, interest expense on both long and short-term debt, interest on customer advances, other financial expenses, and retail companies' interest expense.

9 To compute the Tobin's q we use the market-to-book ratio, the most common proxy for finance average q (Erickson and Whited 2006), plus an additional Tobin's q measure computed by adding to the book value of total assets the market value of equity and subtracting the book value of common equity divided by the book value of total assets. To capture firms' investment opportunities one would ideally account for intangible capital, especially when examining zombie companies with respect to their healthy peers. The Total q developed by Peters and Taylor (2017) would fit this purpose. The latter measure is however especially trained for US data, and Compustat North America data items, on US companies while not for European companies captured via Compustat Global.



There are several examples of well-known public companies that have been in dire straits for several years and would have not being able to survive for long without financial support. 10 The existing literature refers to these occurrences as zombie companies, i.e. business entities, often publicly traded firms, that are unable to cover their debt servicing costs from their current profits over an extended period of time. What are zombie companies, how can we measure them, and what are the existing channels explaining their existence? In this section, we take a global perspective and explore their trend (Figure 2), the drivers and existing channels, and the regulatory framework.

Weobserve a rise in zombie shares over the last 18 years. Figure 2 shows that the share of publicly quoted zombies across Europe and the rest of the world has gone up, from close to zero in the 1990s to roughly 15% in recent years. Interestingly, the phenomenon appeared during the late 1990s early 2000s, historically over the dot-com bubble, both in Europe as in the rest of the world. It however spiked up during the global financial crisis, especially evident in Europe, to then decrease slightly during recent years.

The term zombie firms appeared in reference to the US Savings and Loans crisis (S&Ls) of the 1980s and 1990s (Kane 1989) and the Japanese banking crisis of the 1990s. In the latter historical event, Caballero, Hoshi, and Kashyap (2008) document the phenomenon of forbearance lending, a situation in which large banks kept the credit flowing to otherwise insolvent borrowers, also called zombie firms. Recent studies confirm the link between weakly capitalized banks and zombie firms (Acharya, Eisert, et al. 2019; Schivardi, Sette, and Tabellini 2017), while others document the increasing trend, above observed, and suggest the low interest rates as one potential factor explaining the survival of zombie firms (Banerjee and Hofmann 2018).

On the one hand, a common belief shares the idea that Europe might be a repeat of Japan's experience where weak banks were not sufficiently recapitalized and did not foreclose on zombie borrowers to avoid reporting the losses (Andrews and Petroulakis 2017). On the other hand, banks may also lend to zombie companies because of strong existing relationships. At the same time, in addition to wrong bank lending behaviors and excessive levels of corporate debt, typical among zombie firms, today's zombie conundrum is also characterized by an environment of very low interest rates for long and unconventional monetary policy measures adopted by the central banks in response to the global financial crisis. 11 Thus, at least two channels emerge.

The zombies that are flooding most of our economies are often regarded as troubled companies that under normal economic conditions would exit the market and be replaced by new entrants. Let us consider an economy with and without zombies.

A world without zombie companies consists of businesses that are well-established in an industry and would-be entrants that could eventually enter the market in the future. In the event of a common shock, and in a normal competitive setting, the least performing companies exit the market. In the case of a permanent shock, the economy would adjust to the new equilibrium but a lower number of companies would exist. In an economy populated by zombies the entry and exit dynamics are instead different as such companies are allowed to remain in the market for longer because of the external financial support they receive from creditors, either their banking counterpart or the government. In the latter scenario, there exists a congested market where zombies and healthy firms have to compete under unequal conditions (Hoshi 2006; Caballero, Hoshi, and Kashyap 2008).

Within this theoretical framework, we articulate the channels at work in order to unfold the rationale behind the ongoing presence of zombie companies. The widespread existence of zombie firms is a credit misallocation issue, where credit is allocated to companies that are not economically viable, thus keeping them afloat for longer.

The misallocation can occur from two, related, channels: (i) the banking channel and (ii) the monetary policy channel. The first channel, would see a banking system that is not adequately recapitalized, where banks with equity shortfalls engage in evergreening to avoid loan loss recognition (Caballero, Hoshi, and Kashyap 2008; Acharya, Eisert, et al. 2019; Schivardi, Sette, and Tabellini 2017). The second channel, would consider the persistently low interest rates as potentially reducing the financial pressure on zombie companies to either exit the market or restructure (Banerjee and Hofmann 2018), and to ultimately affect the level and structure of the investment decisions (Gern et al. 2015). In terms of resources misallocation, the existing empirical literature also shows that a decline in the real interest rate increases the dispersion of the return to capital and generates

lower productivity growth as capital inflows are directed to unproductive companies (Gopinath et al. 2017), that a large share of firms are still alive despite low productivity levels (Calligaris et al. 2016), and that companies receiving government subsidies are less likely to die (Satu, Vanhala, and Verín 2020).

The microeconomic setting needs also to be included in the analysis. To account for the persistence of zombie companies, differing regulatory frameworks are also part of the equation. On the one hand, there is a set of countries with efficient regimes that allow to prevent and solve insolvencies, while on the other hand the majority are progressing slowly (McGowan, Andrews, and Millot 2017). In terms of differing legal systems, Haselmann and Wachtel (2010) show that banks operating in a well-functioning legal environment lend relatively more to small and medium-sized enterprises, while in an unsound legal system they tend to lend more to large enterprises and governments. Accounting for differences in the bankruptcy codes, Favara, Schroth, and Valta (2012) show that the prospect of strategic default on the firm's debt affects the firm's equity beta and this effect decreases in countries where debt contracts cannot be easily renegotiated. Efficient reorganization and liquidation procedures are also crucial in the design of financial contracts and firm investment (Rodano, Serrano-Velarde, and Tarantino 2016). Djankov, McLiesh, and Shleifer (2007) highlight specific differences between common law and civil law countries in terms of creditor rights and public registries. In addition, civil law countries, like France and Germany, have developed a high level of protection for creditors in the form of controls over the management of debtor firms, while common law countries, like the UK and USA, have reached a high degree of protection in relation to secured creditors' contractual rights over firms' assets (Deakin, Mollica, and Sarkar 2017). How different countries deal with unviable firms varies over time and depends on unequal contract laws, securities laws, criminal laws, the availability of extrajudicial options, the institutional development of a country (in terms of courts, creditors, banks and government), and the diversity of claims and the degree of information asymmetries (Claessens, Djankov, and Mody 2001).

The existing bankruptcy and restructuring frameworks might however not be fully used in targeting zombies, given that the latter are different to distressed firms, as they are companies with healthy periods in-between unsound years and likely to recover.

The geographical concentration of zombies in the United States, Figure 3, and in Europe, Figure 4, highlights firm-specific differences, but also regulatory and governmental divergences (McGowan, Andrews, and Millot 2017). With respect to the latter, we also observe how industry-specific factors play a role across countries (Figures A2).

Examining the US data set, Figure 3 registers the highest shares of zombie companies, in dark blue, in the US states of Montana, Idaho, Wyoming, Utah, Colorado, Nevada, New Mexico, Texas, Florida, West Virginia, New Jersey and Rhode Island.

From Compustat Global data set, Figure 4 plots the zombie shares for our sample of European countries. The map documents that the countries with the highest share of zombies are Portugal, Greece, Cyprus, Croatia, Macedonia, Slovenia and Slovakia.

3 Determinants of Zombie Firms

3.1 Decision Trees to Classify Zombies

The high dimensions of our data set renders it cumbersome, if not impossible, to analyze the determinants of financially unviable companies based on classical statistical models. Such an approach would imply to make a priori assumptions and rely on a subset of the available variables. In line with Breiman (2001), we use algorithmic modeling to find important variables. In consideration of the large amount of input variables at disposal, we consider decision trees an appealing and intuitive approach to identify the most important determinants out of a broad range of possible explanatory variables. The algorithm underlying the decision tree searches the whole range of explanatory variables and subsequently, i.e., at each iteration, finds the variable that helps classify zombies and no zombies best. Moreover, at each iteration the algorithm searches for the best split - input variable combination that reduces the loss function most. The advantage of a decision tree is its simplicity in combination with outstanding interpretability through elegant visualization. In contrast to classic statistic knowledge-based models, i.e., a Logit model, the tree finds the firm determinants directly from the data without the need for assumptions. Therefore, decision trees provide a novel perspective on the determinants of zombie, distressed, recovered and healthy companies.

The idea of decision trees is to subsequently split the input space X into rectangular segments and provide a decision at each one of those rectangles. Accordingly, in each section, the outcome variable y is modeled with a different constant, e.g., the mean, in regression problems or majority vote in classification problems. The algorithm makes one binary split only for a single input feature at each iteration. After each iteration, the tree repeats the procedure in the new sub-samples.

In order to construct the input space regions, we follow the popular CART algorithm, which finds exclusive, non-overlapping regions R 1 , . . . , R j with a rectangular shape. Consider a sample of input and output GLYPH<0> y, X GLYPH<6> , where y is a discrete variable with classes K and X GLYPH<0> GLYPH<0> x 1 , x 2 , . . . , x p GLYPH<6> includes the input variables. We require the algorithm to automatically find the best input variable and split point s at each iteration. The proportion of the response variable y for each region R j , is thus given by:

ˆ p mk GLYPH<0> 1 N m = x i ∀ R m I GLYPH<0> y i GLYPH<0> k GLYPH<6> , (1)

where I is the indicator function. A standard loss function of the CART algorithm is the Cross-entropy, given by:

L GLYPH<0> p GLYPH<6> GLYPH<0> GLYPH<14> K = k GLYPH<0> 1 ˆ p mk log GLYPH<0> ˆ p mk GLYPH<6> , (2)

where p k is the probability of class k and the impurity reaches its minimum if all observations are classified correctly. However, a direct, contemporaneous computation of the regions by minimizing the loss function is not feasible as the input space can be split

in infinite combinations of sub-rectangles. Therefore, we start with a top-down approach of binary splitting. Assume a first splitting variable l and a splitting point s , we choose the first pair of regions as:

R 1 GLYPH<0> l, s GLYPH<6> GLYPH<0> ρ X ∂ X l & s ξ and R 2 GLYPH<0> l, s GLYPH<6> GLYPH<0> ρ X ∂ X l % s ξ . (3)

Ultimately, we find the splitting variable l and split point s by solving arg max k ˆ p lk . After partitioning the input space in two regions, based on the best splitting variable and split point, the process is repeated within each region. High interpretability provides a prime tool to determine important factors characterizing zombie firms. 12

In a second step, we augment our algorithm and provide multivariate decision trees to delve deeper into the factors that are more conducive to a company being a zombie, distressed, healthy or recovered. In performing this exercise, we account for the fact that zombie companies are mostly growing companies with unsound periods.

We develop a set of decision trees for both geographical areas, the United States and Europe, and we account for time-varying differences to understand whether firm-specific drivers change in response to economic downturns. To do this, we estimate the financial crisis period, 2008-2010, and a financially healthy period, 2015-2018. 13

The decision trees provide the variable name and split point and the % of observations used by the algorithm at each node. The entropy provides a measure of the node purity and the values show the % of non-zombies (left) and zombies (right) after the split. Accordingly, nodes with a deeper color are more pure and show how well the explanatory variable separates the possible categories. I.e., values of GLYPH<18> 0 . 6 , 0 . 4 GLYPH<24> represent a sample with 60% of non-zombies and 40% of zombies after the split. Nodes with a blue color indicate a majority of zombies and vice versa in orange. A white node shows an indecisive split.

3.2 Empirical Evidence: Determinants of Zombie Firms

3.2.1 Europe

We analyze the firm-specific drivers of zombie versus non-zombie publicly listed companies for a sample of 32 European countries. 14 To account for time-varying differences, Figure 5 shows the decision tree results during the global financial crisis, while Figure 6 observes changes during the years 2015-2018, a non-crisis period.

At first, we document similarities between the crisis and non-crisis years, underlining that regardless of economic downturns specific drivers persist. Among the European countries two aspects stand out, (i) Income-related variables are the main firm-specific determinants, followed by (ii) Debt-related variables. In terms of income-related variables, operating income ( oiadp ) allows for the most crucial binary split to classify zombie

companies in Europe, indicating that for low values of operating income the tree predicts that the company is likely a zombie, vice versa for higher values thus leading to orange-colored nodes. Among other income-specific variables, income before extraordinary items, ib , pretax income, pi , and non-operating income, nopi , are also recurrent in the higher splits. The decision tree algorithm allows us, contrary to classical statistical models, to detect and show which parts of a firm income likely determine the zombie status. In terms of debt-related variables, liabilities total, lt , is instead the most decisive driver. In this regard, we recall that in order to avoid any potential simultaneity in our results we exclude from the algorithm the variables related to the zombie definition.

In addition, the algorithm highlights how companies with low operating income values, high total liabilities and high levels of common stock are classified as zombies, likewise during crisis and non-crisis years. We thus confirm that the zombie phenomenon in Europe is well described by the presence of overly indebted firms, where a combination of low income, low returns and a high debt ratio is indeed a typical feature. In this regard, Hoshi (2006) documents that Japanese zombie companies are smaller firms, less profitable, more indebted, more likely to be found in non-manufacturing industries and often located outside large metropolitan areas. With respect to geographic-specific factors we refer to Section 3.5, where a fixed-effects logistic regression model that incorporates country fixed effects is presented. In our case, no specific industries are returned by the algorithm to categorize zombies in Europe, and interestingly firm size is not chosen among the relevant determinants.

Another interesting aspect is that during the crisis a firm is classified as a zombie, if it has low operating income, high debts, high common stock and high investing activities, ivncf , while in healthy years investing activities are replaced by a high share price close value. The latter result is mostly explained by the crowding out of healthy firms' investments during crisis periods (Banerjee and Hofmann 2018).

Legend: oiadp Operating income after depreciation, lt Liabilities total, ib Income before extraordinary items, cstk Common stock, nopi Nonoperating income, bl Book leverage, ero Other equity reserves, lco Current liabilities other, ivncf Investing activities net cash flow, roa Return on assets, nbl Net book leverage, txt Total income taxes.

Legend: oiadp Operating income after depreciation, cstk Common stock, pi Pretax income, dpact Depreciation and amortization, nopi Nonoperating income, lt Liabilities total, epsincon Earnings per share including extraordinary items, prcc _ f Stock price close fiscal, roa Return on assets.

3.2.2 United States

Implementing a decision tree based on US data sheds light on the zombie phenomenon in the US, an unexplored country sample by existing studies. First, the results show no major differences between the two time periods observed. Second, the decision trees predict that (i) Stock prices and (ii) Dividends are the main drivers that classify zombies versus non-zombies. Consequently, the variables that define zombies in the US are more performance related when compared to their European counterparts. As reported by Skinner and Soltes (2011), dividends provide information about earnings quality and future earning prospects and thus zombies are determined by conservative dividend policies. Third, in both time periods the main root node returns the variable stock price low, prcl , as the most important determinant. Last, in both time frames industry-specific variables are influential in classifying zombies versus non-zombies. In particular, during the financial crisis real estate is mostly prominent and, to a lesser extent, software services, while during healthy years real estate remains decisive, followed by the energy industry.

In addition, our findings underline clear differences in classifying zombies in Europe versus zombies in the United States. We recall, from the above section, that income-

related and debt-related variables are the main drivers categorizing publicly listed European zombies. This result can be explained by intrinsic differences between US and European public corporations, and by differing regulatory frameworks. In this regard, looking at insolvency regimes, we observe that efficient regimes are more likely to facilitate the exit or downsizing of zombie-like firms and that differences in corporate restructuring are however evident both across European countries as between Europe and the US (McGowan, Andrews, and Millot 2017). As examined by Brouwer (2006), the method of survival differs, where in the United States reorganization is the most efficient method to resuscitate a company, while in Europe fewer bankruptcies result in reorganization. This can further explain the prevalence of zombies across Europe, in contrast to the US, as examined in Section 3.4.

To further understand the implications of our findings, we draw upon the existing empirical finance literature. The latter however solely examines financially distressed companies, or companies that are close to default. The low stock prices are well documented by Garlappi and Yan (2011) who show the link with high default probabilities, Campbell, Hilscher, and Szilagyi (2008) confirm that distressed firms typically have low prices per share, while H. DeAngelo and L. DeAngelo (1990) document that distressed firms tend to cut their dividends.

Legend: prcl _ c Stock price low calendar, dvpsx _ c Dividends per share ex-date calendar, prcc _ f Stock price close fiscal, cshtr _ c Common shares traded calendar, prcl _ c Stock price low calendar, prcc _ c Stock price close calendar, prch _ c Stock price high calendar, real _ estate _ inv REITs and other real estate investments, software software and services.

Legend: prcl _ f Stock price low fiscal, dvpsp _ f Dividends per share pay date fiscal, dvpsx _ f Dividends per share ex-date fiscal, csho Common shares outstanding, cshtr _ f Common shares traded fiscal, cshtr _ c Common shares traded calendar, prcl _ c Stock price low calendar, real _ estate _ inv REITs and other real estate investments, energy _ ind Energy, energy equipment, services, and others.

3.3 Empirical Evidence: Determinants of Distressed Firms

3.3.1 Europe

Figure 9 provides the results of the firm-specific drivers of distressed versus non-distressed publicly listed companies in 32 European countries during the global financial crisis, while Figure 10 analyzes a financially healthy time period, 2015-2018. The main findings are captured by two aspects: (i) Leverage, and (ii) Income. Leverage-related variables show similarities, while income-related variables highlight important differences.

With respect to leverage, book leverage, bl , is one key variable that is returned by both decision trees in their root node, the node in white color, which represents the most important split to classify a company as distressed or non-distressed. With respect to income, the one variable that is returned in the European decision trees' root node classifying zombies versus non-zombies is operating income after depreciation, oiadp .

Leverage-related variables are likewise selected to classify financially distressed firms and zombie firms. In the latter case, the liabilities total, lt , is another very decisive and recurring explanatory variable returned by the classification tree algorithm to capture

zombie companies in Europe during both healthy and crisis time periods. Therefore, both distressed and zombies have a debt-level component in their financial structure that makes them similar, but at the same time income-specific items are especially categorizing zombies versus non-zombies. From the previous section, we recall that other incomerelated variables such as pretax income, pi , non-operating income, nopi , and income before extraordinary items, ib , are also often recurring in the higher splits.

These findings show that both zombie and distressed firms have accrued debts weighting down on their operating activities. At the same time, given their level of operating income, we observe from the data processing that zombie companies are likely to recover rather than dying. Distressed companies appear instead at a different stage of their unviability, as also suggested from Table 1, making them more likely to default or enter bankruptcy in order to protect their assets from creditors.

Among other explanatory variables that are relevant to classify distressed versus nondistressed companies, return on assets, roa , and stock price close, prcc , are often identified during the crisis years, Figure 9, as well as during healthy periods, Figure 10, followed by the level of working capital, wcap , especially during the crisis.

On the one hand, the corporate finance literature documents that the return on assets is an important financial ratio predicting corporate distress, as it captures an ongoing underperformance due to operating decisions or external forces, and shows that some of the most salient characteristics of distressed companies are low market value, high leverage, cash flow problems and prices sensitive to negative conditions (Chan and Chen 1991). On the other hand, there is no evidence yet on the specific differences or similarities between zombies and distressed. Our findings thus indicate that there are some specific parts of the income of a company, such as pretax income, non-operating income and income before extraordinary items, that distinguishes zombie from non-zombie firms and that can be used as a diagnostic tool to better categorize zombie companies in Europe. Specific parts of the debt of a company, such as liabilities total and book leverage, can instead classify both the distress stage and the zombie stage. In this regard, a set of descriptive statistics (Table 1) further document that distressed European firms have a higher leverage, net leverage, asset tangibility and operating profit than zombie firms.

Legend: bl Book leverage, roa Return on assets, prcc _ f Stock price close fiscal, lt Liabilities total, wcap Working capital, dlc Total debt in current liabilities, ero Other equity reserves, cshpria Common shares for basic earnings per share.

Legend: bl Book leverage, prcc _ f Stock price close fiscal, roa Return on assets, epsincon Earnings per share including extraordinary items, lt Liabilities total, wcap Working capital.

3.3.2 United States

Figure 11 shows the results of the firm-specific determinants of distressed versus nondistressed companies in the United States during the crisis years, while Figure 12 documents the main drivers during a period of time that we consider as financially healthy, from 2015 to 2018. In the United States, the main findings are captured by: (i) Stock prices, and (ii) Dividends. The interesting aspect is that stock-related variables and dividends-related variables mostly highlight existing similarities between distressed and zombies. The main differences are instead captured by industry-specific factors.

With respect to stock-related determinants, stock price low, prcl , is the main root node variable returned by the decision tree algorithm for both the distressed and the zombie companies in the United States during the crisis and healthy years. With respect to dividends-related drivers, dividends per share, dvpsx , is often returned in the higher splits of the trees for both distressed and zombie firms. In this regard, the empirical finance literature examining companies close to default suggests a relationship between high default probabilities and low stock prices, pointing out that a low stock price is an indicator of the financially unhealthy status of the company reflected in its market value (Garlappi and Yan 2011). Looking at a sample of NYSE-listed firms, H. DeAngelo and L. DeAngelo (1990) document that the managers of financially distressed companies responded to the distress stage with early and aggressive dividend reductions. Denis and Osobov (2008) document that in the US the propensity to pay dividends is higher among larger and more profitable firms. Kahle and Stulz (2017) however observe a change in US public corporations from the 1970s to today and document that nowadays payouts to shareholders are mostly in the form of share repurchases.

Of the main differing characteristics, the results highlight the role of specific industries. On the one hand, industries are not picked up by the algorithm of distressed versus non-distressed firms, but on the other hand they appear in the zombie classification as decisive node to distinguish a zombie from a non-zombie. In particular, real estate investments and, to a lesser extent, software, are the two industry-related variables returned by the crisis decision tree, while energy industrial and real estate investments are captured during healthy years (Figures 7 and 8). The latter result can potentially relate to industry-wide declines, where firms in highly leveraged industries are less able to sell their assets, and overall firms can become financially unviable also because of an industry downturn (Asquith, Gertner, and Scharfstein 1994).

The results so far documented remain robust to a second, alternative, zombie definition that follows Banerjee and Hofmann (2018). Additional results are provided in the Appendix, where Figure A4 shows the firm-specific determinants for the European sample, while Figure A5 for the US sample.

Legend: prcl _ c Stock price low calendar, prcc _ f Stock price close fiscal, dvpsx _ f Dividends per share by ex-date fiscal, cshtr _ c Common shares traded calendar, prcl _ f Stock price low fiscal, cshtr _ f Common shares traded fiscal, csho Common shares outstanding, prcc _ c Stock price close calendar.

Legend: prcl _ f Stock price low fiscal, dvpsx _ f Dividends per share by ex-date fiscal, csho Common shares outstanding, prcc _ f Stock price close fiscal, cshtr _ c Common shares traded calendar, cshtr _ f Common shares traded fiscal, prcc _ c Stock price close calendar.

3.4 Multi-Class Analysis: Determinants of Zombie, Distressed, Recovered, and Healthy Firms

3.4.1 Europe

The multi-class follows the same structure of the binary trees. The importance of the nodes and items they inherit are the same and at each iteration the algorithm finds a variable that separates one category from the others. The impurity and the item value, however, inherit four values. From left to right, the values describe the proportion of healthy, distressed, zombie and recovered companies within the node and are crucial to clarify how well the explaining variable separates the firms' categories. The categories of healthy, distressed, zombie and recovered are represented in orange, green, blue and purple color, respectively. A dark blue colored node contains mostly zombies. In contrast to the binary trees, the multi-class has a horizontal structure where the if-else reasoning changes. We follow the tree upwards if the statement is True and downwards otherwise. 15

The interpretation is as follows: the predicted category has, after the initial split, the most significant proportion in the new sub-input space, therefore if the node predicts a healthy company the algorithm finds the most significant decrease in the loss function by separating the good companies from the others. 16

Figure 13 documents the crisis years, while Figure 14 the non-crisis, 2015-2018.

Of the main findings, similarly to the binary trees, in both time periods the root node variable is operating income after depreciation, oiadp , underlining the importance of income-related drivers for the first split. An outcome that yields relevant information. Smaller values of operating income lead to zombie firms, blue node, while larger values to healthy companies, orange node. A firm with low operating income and low stock closing price is also likely a zombie, while a company with positive values of operating income, low book leverage and high return on assets is likely healthy. While, higher values of operating income and book leverage and low return on assets predicts a distressed company. If the firm has low return on assets and also low retained earnings, the algorithm confirms the likelihood of being distressed. We however underline that most of the higher splits are inconclusive as the color of the nodes is very light, indicating the indecisiveness of the algorithm in separating the categories. In addition, among the four analyzed classes those that are better represented are those of the healthy and the zombies.

The results during non-crisis years are similar with respect to the indecisiveness of the algorithm, but differently to the crisis period a combination of income, leverage and stock-related variables compose the main drivers.

This figure shows the multi-classification tree for Europe, from 2008 to 2010. The main measure is used to identify the zombies. Distressed are measured with the z-score (Altman 1968). Healthy are those with an interest coverage ratio above 1. Recovered are those that exited the zombie status. Higher splits provide higher importance for the decision. The decision iteration of the CART algorithm is provided at the top of each node. The nodes purity is given by a higher entropy and a darker color.

Legend: oiadp Operating income after depreciation, lt Liabilities total, ivncf Investment activities net cash flow, epsincon Earnings per share including extraordinary items, epsexcon Earnings per share excluding extraordinary items, wcap Working capital, cshoi Common shares outstanding interim, dlc Debt in current liabilities total, xacc Accrued expenses, txt Total income taxes, cstk Common stock, txditc Deferred income taxes, bl book leverage, ero Other equity reserves, roa , Return on assets, prcc _ f Stock price close, re Retained earnings. 27

Legend: oiadp Operating income after depreciation, nbl Net book leverage, lt Liabilities total, cshoi Common shares outstanding interim, epsincon Earnings per share including extraordinary items, prcc _ f Stock price close fiscal, epsexcon Earnings per share excluding extraordinary items, roe Return on equity, roa Return on assets, re Retained earnings, ib Income before extraordinary items, txt Total income taxes, bl Book leverage, at Total assets, np Notes payable short-term borrowing.

3.4.2 United States

Figure 15 documents the results of the multi-class tree during the financial crisis, while Figure 16 shows the main drivers of US public corporations during non-crisis years.

We find very similar results to the distressed versus non-distressed trees. Stockrelated and dividends-related variables are the main drivers categorizing healthy versus distressed-type of firms. The main root node, white colored, is stock price low, prcl . In this regard, smaller values of stock price low lead to distressed firms, green node, while higher values of stock price low lead to healthy companies, orange node. At the same time, a company with higher stock price low and dividends per share is likely a healthy firm. If the latter has lower values of common shares traded and shares outstanding the algorithm confirms the likelihood of being healthy. Among the industries, real estate further categorizes healthy versus zombies.

The main distressed-type of firms drivers are documented in the True upward branch, signalling that if a company has lower values of stock price low and low stock price close it is likely a distressed. The results further show that the algorithm is very decisive in predicting distressed and healthy firms via stock-specific characteristics, while not enough to predict those firms that were zombie once and then recovered. Zombie-type companies are instead very underrepresented, again indicating that, contrary to European public corporations, the zombie phenomenon in the US is less of a concern, where the distressed populate much of the sample.

Our findings show no major differences between crisis and non-crisis years. Figure 16 confirms stock and dividends-related variables as main firm-specific determinants classifying distressed versus healthy companies. The main difference sees dividends per share as root node, dvpsx . If a company has low values of dividends per share and low stock price close it is likely a distressed as during healthy times, whereas if it shows higher values of dividends per share and low real estate concentration it is likely a healthy firm. During non-crisis years, the prevalence of distressed and healthy firms is evident.

The decision trees allow us to not only put the zombie companies under the magnifying glass, but to also compare them with other classes of companies like the healthy, the distressed, and the recovered. This classification process let us make comparisons, look for relevant differences and similarities in firm-specific drivers and underline important patterns. In this respect, our findings suggest that zombie companies are at a different stage of their financial unviability in comparison to distressed firms that show the typical characteristics of firms close to default. Overall, the findings suggest that zombie companies are mostly a European phenomenon.

This figure shows the multi-class decision tree for the US, from 2008 to 2010. The main measure is used to identify the zombies. Distressed are measured with the z-score (Altman 1968). Healthy are those with an interest coverage ratio above 1. Recovered are those that exited the zombie status. Higher splits provide higher importance for the decision. The decision iteration of the CART algorithm is provided at the top of each node. The nodes purity is given by a higher entropy and by a darker color.

Legend: prcl _ f Stock price low fiscal, prcc _ f Stock price close fiscal, dvpsx _ f Dividends per share ex-date fiscal, prcc _ c Stock price close calendar, csho Common shares outstanding, prch _ f Stock price high fiscal, cshtr _ f Common shares traded fiscal, cshtr _ c Common shares traded calendar, prch _ c Stock price high calendar.

This figure shows the multi-class decision tree for the US, from 2015 to 2018. The main measure is used to identify the zombies. Distressed are measured with the z-score (Altman 1968). Healthy are those with an interest coverage ratio above 1. Recovered are those that exited the zombie status. Higher splits provide higher importance for the decision. The decision iteration of the CART algorithm is provided at the top of each node. The nodes purity is given by a higher entropy and by a darker color.

Legend: dvpsx _ f Dividends per share ex-date fiscal, prcc _ c Stock price close calendar, cshtr _ c Common shares traded calendar, csho Common shares outstanding, prch _ c Stock price high calendar, prcl _ f Stock price low fiscal, prch _ f Stock price high fiscal, dvpsp _ f Dividends per share by payable date fiscal.

3.5 Benchmark Analysis: Logistic Models

In this section, we analyze the performance of the firm-specific variables detected by the decision tree algorithm using a fixed-effects logistic regression model. Table 2 shows the results for the European country sample, while Table 3 reports those for the US.

In all models, we provide time fixed effects but also incorporate country and industry fixed effects separately. Additionally, we incorporate, besides country fixed-effects, industry fixed-effects as they arise in the individual decision trees. In both locations, Europe and the United States, the industry has an extraordinary impact. Also, we provide regression models for zombie and distressed companies in order to analyze firm-specific differences and similarities.

We find that most variables chosen by the decision tree algorithm provide significant estimates also in the logistic models. Additionally, the sign of the coefficient estimates is mostly in line with the trees. More specifically, we document that income-related variables, such as operating income and pretax income, are a crucial indicator for zombie companies, where an increase in income decreases the probability of a company being a zombie. Additionally, the income variables distinguish zombie companies from distressed ones, as income variables do not significantly impact distressed companies. Also, we observe that return on assets and the share price provide significant determinants for distressed but not for zombie companies. However, besides the differences, we also find similarities, especially with respect to stock market variables and debt in liabilities. The higher significance level of total debt in liabilities for distressed companies is in line with our argumentation that distressed companies, in contrast to zombie companies, are in a more advanced stage of their financial unviability.

In contrast to the income-driven European companies, we find that the shares' value significantly determines zombie and distressed companies in the United States. Accordingly, lower stock prices predict zombie and distressed companies. Similarly to Europe, industry-specific factors do play a relevant role also in the United States. We also document differences among the US states.

Nonetheless, the fixed-effects logistic regression combined with the decision trees provides novel insights to zombie and distressed companies' firm-specific characteristics. Moreover, the regression approach shows that the decision tree finds essential variables from a sizeable input space and correctly splits the trees similar to the coefficient estimates sign. Therefore, the decision trees provide an excellent tool for detecting determinants of zombie and distressed companies within the context of big data.



4 Conclusion

The zombie phenomenon is not a myth, rather a reality affecting several countries globally since the late 1990s. The way this phenomenon manifest itself however differs from one geographical area to another, given firm-specific differences, industry-specific factors, and diverging regulatory frameworks. This study examines the firm-specific determinants of zombie companies from an international perspective over several business cycles. The aim is to identify differences and similarities among zombie, distressed, healthy, and recovered zombies and understand whether and to which extent firm and country-specific characteristics change during crisis and non-crisis years.

We use two exhaustive firm-level data sets, Compustat Global and Compustat North America, on a sample of publicly listed companies from the United States and 32 European countries over a period of twenty-two years. The high-dimensional data allows us to feed a well-trained supervised learning algorithm that returns us a series of valuable information on zombie and non-zombie companies. We refrain from any a priori assumptions and instead use algorithmic modeling to find the main drivers. This method, based on classification trees, gives us the privilege to put the zombies under the magnifying glass, monitor them over time and across countries, and add the classes of the distressed, healthy and recovered into a multi-class tree-like model.

The results document that US zombie firms differ from their European peers on a number of firm and industry-specific factors. In particular, income and leverage-related variables are the main drivers classifying zombie companies in Europe, while dividends and stock-related variables are the most important to categorize US zombies. On the one hand, the decision trees categorize the US zombie companies as low-priced stock and low dividends per share business entities that are mostly populating the real estate and energy industry, while on the other hand the European zombies are described as entities with low operating income and high debts weighing down the recovery process.

Zombie companies are often misclassified as financially distressed companies, making the zombie identification a challenging task that lacks a disciplined approach. To account for this, we further examine distressed-type of firms and compare them to the zombies. The findings show that zombie and distressed are not comparable types of companies, rather companies at a different stage of their financial unviability. Differently to existing studies, we detect specific persisting drivers. The decision trees suggest that both distressed and zombie firms in Europe have likewise a high debt-level component in their financial structure, but income-specific items especially categorize zombies, while leverage-related variables classify the distressed. In the US, stock and dividends-related variables likewise categorize distressed and zombies, while industry-specific factors denote notable differences. We find no major differences between crisis and non-crisis years.

In addition, the results document that zombification is especially a European phenomenon, while distressed-type of firms mostly populate the US economy. We further complement the classification trees with a series of logistic regressions on the various classes of identified companies. Our results remain robust to an alternative zombie measure that considers market expectations.

Overall, this paper identifies clear differences in classifying zombies in Europe versus zombies in the United States, pointing out intrinsic differences between US and European public corporations and differing regulatory frameworks. Contrary to existing methods, classification trees allow us to categorize zombies and non-zombies and observe salient firm-specific characteristics that can be used as policy-relevant diagnostic tool to better classify and cope with diverging zombies across countries. Further research envisages an extension of the method to account for country-specific and regulatory factors.

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A Appendix

A.1 Variables Description




A.2 Descriptive Statistics

Share of Zombie Companies by Industry

A.3 Measuring Zombies

The strand of literature focusing on zombie companies provides different approaches to identifying a company as a zombie, each one of them with its own advantages and drawbacks. The zombie definition itself, together with data limitations, explains the existing measurement challenges.

One of the first measures originates from the study of Caballero, Hoshi, and Kashyap (2008) on Japanese companies during the 1990s banking crisis. The authors classify a company as a zombie whenever it receives subsidized credit at an interest rate that is below the one applied to the most creditworthy companies. The actual interest payments made by the companies are then compared to an estimated benchmark, R GLYPH<152> , based on the firm's debt structure and market prime rate. The minimum required interest payment for each firm i in year t , R GLYPH<152> it , is defined as:

R GLYPH<152> it GLYPH<0> rs t GLYPH<14> 1 BS it GLYPH<14> 1 GLYPH<17> GLYPH<3> 1 5 5 = j GLYPH<0> 1 rl t GLYPH<14> j GLYPH<9> BL it GLYPH<14> 1 GLYPH<17> rcb min over last 5 years, t GLYPH<18> Bonds it GLYPH<14> 1 , (1)

where BS it , BL it , and Bonds it represent short-term loans (less than one year), long-term bank loans (more than one year), and total bonds outstanding (including convertible bonds and warrant-attached bonds), respectively, for firm i at end of year t ; while rs t , rl t , and rcb min over last 5 years, t represent the average short-term prime rate in year t , the average longterm prime rate in year t , and the minimum coupon rate on any convertible corporate bond issued in the last five years before t .

Given that we are interested in examining the determinants of zombie companies from an international perspective, and given the data constraints, replicating such measure does not fit our study. 17 As noted in Banerjee and Hofmann (2018), by employing this measure one would encounter three potential limitations: (i) identifying with precision the subsidized credit granted by the banks to the companies would be a challenge, (ii) banks may grant subsidised credit for other reasons, such as long-standing relationships, and (iii) when interest rates are very low for longer periods, subsidized lending rates would have to be near zero or even negative.

For these reasons, the more recent zombie literature often adopts a definition that relies on the accounting information of such firms to capture their unproductive nature, their age, and in some cases their future growth potential. The most widely used measure evolved around the interest coverage ratio, initially used in the study of Adalet McGowan, Andrews, and Millot (2018), and subsequently used in other academic studies and central banks reports. The interest coverage ratio is a measure that goes beyond the debt composition of the company and looks at the operating income and at the persistency of the condition of distress . A company is considered a zombie whenever its ICR it ∃ 1 for 3 consecutive years and age ∋ 10 years . In Banerjee and Hofmann (2018) the latter measure is complemented with an additional factor, the company's future growth potential, captured with the Tobin's q. In Banerjee and Hofmann (2020) they dismiss the age factor. In Acharya, Crosignani, et al. (2019) a company is considered a zombie if it meets two criteria: GLYPH<0> i GLYPH<6> the firm's ICR is below the median and its leverage ratio is above the median, GLYPH<0> ii GLYPH<6> the share of interest expenses relative to the sum of its outstanding loans, credit, and bonds in a given year is below the interest paid by the most creditworthy firms (Acharya, Eisert, et al. 2019). The latter criterion follows the subsidised credit measure of Caballero, Hoshi, and Kashyap (2008). In our study, we follow Adalet McGowan, Andrews, and Millot (2018) as main definition and we compute the Banerjee and Hofmann (2018) measure as robustness.

A.4 Decision Tree Example

Let us assume that we want to predict if a person pays back a credit and we have the age and account balance of that person. The tree searches the variable age and account balance for a split point that helps to separate the persons who repay the credit from those who do not. As an arbitrary example, the tree may split the variable account balance at $1905, meaning that the tree separates all persons with an account balance lower than $1905 from those with a higher account balance. Therefore, the input space X is separated. This searches for the best variable and iterates the split point until a stopping criteria is fulfilled. Note that in the next step the tree may separate out the input space of persons with less than $1905 and an age higher than 54. Below, we show how this artificial example would translate into a simple decision tree setting:

A.5 Additional Results

Figure A4 shows the firm-specific characteristics of zombie vs. non-zombie in Europe using an alternative zombie definition that follows Banerjee and Hofmann (2018). Data relates to the crisis years, 2008-2010, in the upper tree, and healthy years, 2015-2018, in the lower tree.

Legend: oiadp Operating income after depreciation, cme Common market equity, pi Pretax income, cstk Common stock, bl Book leverage, nopi Nonoperating income, txt Total income taxes, roa Return on assets, dpact Depreciation, depletion and amortization, fincf Financing activities net cash flow.

Legend: oiadp Operating income after depreciation, cme Common market equity, pi Pretax income, cstk Common stock, roa Return on assets, nopi Nonoperating income, dpact Depreciation, depletion and amortization, fincf Financing activities net cash flow.

Figure A6 shows the firm-specific characteristics of zombie vs. non-zombie in Europe in the upper tree and in the United States in the lower tree. The first zombie definition is here used. Data refer to the whole period of observation, 2006-2018.

Legend: oiadp Operating income after depreciation, cstk Common stock, pi Pretax income, dlc Total current liabilities, bl Book leverage, re Retained earnings, nopi Nonoperating income, dpact Depreciation, depletion and amortization, epsexcon Earnings per share excluding extraordinary items, roa , Return on assets, prcl _ c Stock price low calendar, prcc _ f Stock price close fiscal, dvpsx _ f Dividends per share by ex-date fiscal, cshtr _ f Common shares traded fiscal, cshtr _ c Common shares traded calendar.

Figure A7 shows the firm-specific characteristics of distressed vs. non-distressed firms in Europe in the upper tree and in the United States in the lower tree. The first zombie definition is here used. Data refer to the whole period of observation, 2006-2018.

Legend: nbl Net book leverage, roa Return on assets, lt Liabilities total, re Retained earnings, prcc _ f Stock price close fiscal, cstk Common stock, prcl _ f Stock price low fiscal, dvpsx _ f Dividends per share by ex-date fiscal, dvpsx _ c Dividends per share by ex-date calendar, cshtr _ f Common shares traded fiscal, cshtr _ c Common shares traded calendar, csho Common shares outstanding.

Legend: prcl _ f Stock price low fiscal, prcc _ f Stock price close fiscal, dvpsx _ f Dividends per share ex-date fiscal, prcc _ c Stock price close calendar, csho Common shares outstanding, prch _ f Stock price high fiscal, cshtr _ f Common shares traded fiscal, cshtr _ c Common shares traded calendar, prch _ c Stock price high calendar.

Legend: oiadp Operating income after depreciation, nbl Net book leverage, lt Liabilities total, ivncf Investment activities net cash flow, epsincon Earnings per share including extraordinary items, epsexcon Earnings per share excluding extraordinary items, wcap Working capital, cshoi Common shares outstanding interim, dlc Total debt in current liabilities, cstk Common stock, bl Book leverage, ero Equity reserves others, roa , Return on assets, prcc _ f Stock price close fiscal, re Retained earnings.